Faster Quantum Algorithm to simulate Fermionic Quantum Field Theory

TL;DR

This paper introduces a faster quantum algorithm for preparing particle states in Fermionic Quantum Field Theory simulations, significantly reducing the computational complexity compared to previous methods.

Contribution

The authors develop a novel matrix product state-based algorithm that accelerates state preparation in Fermionic QFT simulations, applicable to one-dimensional models.

Findings

Achieves $O( ext{epsilon}^{-3.23})$ gate complexity for single-species particles.

Surpasses previous methods with $O( ext{epsilon}^{-8})$ complexity.

Capable of simulating quantum phases disconnected from the free theory.

Abstract

In quantum algorithms discovered so far for simulating scattering processes in quantum field theories, state preparation is the slowest step. We present a new algorithm for preparing particle states to use in simulation of Fermionic Quantum Field Theory (QFT) on a quantum computer, which is based on the matrix product state ansatz. We apply this to the massive Gross-Neveu model in one spatial dimension to illustrate the algorithm, but we believe the same algorithm with slight modifications can be used to simulate any one-dimensional massive Fermionic QFT. In the case where the number of particle species is one, our algorithm can prepare particle states using $O\left( \epsilon^{-3.23\ldots}\right)$ gates, which is much faster than previous known results, namely $O\left(\epsilon^{-8-o\left(1\right)}\right)$. Furthermore, unlike previous methods which were based on adiabatic state preparation, the method given here should be able to simulate quantum phases unconnected to the free theory.